Module II Types of Spatial Data Analysis

Introduction

Welcome to Module II of our Spatial Statistics and Disease Mapping course! Building upon the foundations of spatial statistics from Module I, we now delve into the different types of spatial data and the corresponding analytical techniques. This module focuses on understanding the methods we can use to analyze different spatial data types, without the R code demonstrations, and provides a conceptual understanding with practical examples.

1. Types of Spatial Data and Their Analysis Methods

In this module, we’ll explore the main types of spatial data: areal (lattice), geostatistical, and point pattern data, alongside the specific analytical methods used to address different spatial questions.

1.1 Areal Data (Lattice Data) Analysis

Areal data is spatially aggregated data within predefined areas, such as administrative boundaries or census tracts.

1.1.1 Spatial Autocorrelation

• Definition: Spatial autocorrelation is the measure of similarity between values at locations based on their proximity. It assesses whether values at nearby areas tend to be more similar than those farther away.
• Measures: Common measures include Moran’s I and Geary’s C, which quantify the degree of spatial clustering.
• Real-World Examples:
  • Public Health: Analyzing the spatial distribution of disease rates across regions. For example, mapping areas with higher rates of diabetes and if there is a spatial pattern of higher rates.
  • Socioeconomics: Examining if neighboring census tracts have similar average income levels, using spatial data from surveys.
  • Environmental Science: Studying if neighboring areas have similar levels of deforestation based on satellite data.

1.1.2 Spatial Regression Models

• Definition: Spatial regression models analyze relationships between a response variable and explanatory variables while explicitly accounting for spatial dependencies.
• Models: Includes spatial lag models, spatial error models, and geographically weighted regression (GWR).
• Real-World Examples:
  • Public Health: Modeling the relationship between access to healthcare facilities and mortality rates across administrative areas, considering spatial clustering of mortality.
  • Socioeconomics: Assessing the relationship between socioeconomic factors and crime rates across police districts, accounting for spatial spillovers of crime.
  • Environmental Science: Modeling the impact of land use on biodiversity, considering spatial correlation of vegetation between adjacent regions.

1.1.3 Disease Mapping

• Definition: Disease mapping aims to estimate and visualize the spatial distribution of disease risk. It is about identifying areas with higher or lower risk and assessing factors influencing those risks.
• Models: Bayesian hierarchical models are often used for disease mapping.
• Real-World Examples:
  • Public Health: Mapping disease prevalence or incidence in different areas using survey data.
  • Public Health: Creating maps to monitor temporal change in the geographical distribution of malaria.
  • Environmental Health: Mapping areas with increased risk of environmental hazards based on surveys and environmental data

1.2 Geostatistical Data Analysis

Geostatistical data represent continuous variables observed at specific locations across a spatial field. The focus is often on predicting values at unobserved locations.

1.2.1 Kriging

• Definition: Kriging is a geostatistical interpolation technique that predicts values at unsampled locations based on spatial correlation. It provides not just predictions but also their associated uncertainty.
• Real-World Examples:
  • Public Health: Estimating the spatial distribution of air pollution across a city using measurements from monitoring stations.
  • Environmental Science: Predicting soil contamination levels in a region using sample data at different locations
  • Agricultural Science: Mapping soil nutrient concentrations based on data from field samples.

1.2.2 Variogram Analysis

• Definition: Variogram analysis explores the spatial dependence as a function of distance, providing insights into how spatial correlation decays with increasing distance.
• Real-World Examples:
  • Public Health: Analyzing how quickly incidence of disease changes with distance between observations.
  • Environmental Science: Studying how the concentrations of pollutants in groundwater vary with distance.
  • Geoscience: Examining the spatial variability of soil properties.

1.2.3 Spatial Regression and Prediction

• Definition: Spatial regression methods for geostatistical data combine explanatory variables with spatial effects to make predictions, especially useful when local and global trends exist.
• Real-World Examples:
  • Public Health: Modeling the risk of vector-borne diseases based on environmental factors, accounting for spatial correlation of risk across locations.
  • Environmental Science: Predicting biodiversity using habitat variables, considering spatial dependence between nearby areas.
• Agricultural Science: Modeling crop yields using climate and soil data, with spatial dependence between observations.

1.3 Point Pattern Data Analysis

Point pattern data represent locations of events in space, often without reference to area. Analysis focuses on the spatial distribution of events.

1.3.1 Point Pattern Intensity

• Definition: Intensity refers to the number of events per unit area. Analysis reveals where events are more or less concentrated.
• Real-World Examples:
  • Public Health: Assessing intensity of emergency calls in a city to allocate resources.
  • Urban Planning: Evaluating the density of businesses in different areas of a city.
  • Ecology: Examining the intensity of animal nests in a forest to understand distribution.

1.3.2 Nearest Neighbor Analysis

• Definition: Nearest neighbor analysis calculates distances between points and their nearest neighbors to determine clustering, dispersion, or randomness.
• Real-World Examples:
  • Public Health: Determining if disease cases are clustered, which may indicate an outbreak or a point source of infection.
  • Retail Analysis: Studying the proximity of competing retail outlets.
  • Ecology: Examining the distribution of different tree species.

1.3.3 Spatial Point Process Models

• Definition: Spatial point process models use stochastic models to describe the mechanism that generate point patterns.
• Real-World Examples:
  • Public Health: Modeling distribution of infectious disease cases, revealing factors that influence spread.
  • Criminology: Modeling spatial distribution of crime to understand risk factors and inform police strategies.
  • Ecology: Understanding spatial distribution of animal nests and factors that influence it.

2. Example: Disease Analysis

Let’s consider disease as an example:

• Areal Data: We might have disease rates by administrative region. We can use spatial autocorrelation to assess if high-risk areas cluster, or spatial regression to see the relationship between risk and local risk factors.
• Geostatistical Data: If we have disease risk indicators measured at different points, we can use kriging to predict and map disease risk in unmeasured areas.
• Point Pattern Data: Individual disease locations would enable us to use methods for point patterns to assess whether cases cluster and help us investigate the spread of disease.

3. Conclusion and Transition to Module III

Module II covered core spatial analysis methods and their applications based on different spatial data types (areal, geostatistical, and point patterns). This provides a strong foundation for analyzing spatial patterns, understanding relationships and exploring spatial processes in the real world.

In Module III, we will shift our focus to Regression Analysis using Spatial Methods. We will review linear regression, introduce spatial regression models (spatial lag and spatial error models), explore their application with survey data, and focus on how to interpret and assess these model outputs. We will be combining the concepts of spatial analysis from module II with regression methods in module III. ```